Decline Curve Analysis Considering Non Laminar Flow in Two Porosity Systems
- Jesus Rodriguez-Roman (Petroleos Mexicanos) | Rodolfo Camacho Velazquez (Pemex)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2005
- Document Type
- Journal Paper
- 478 - 490
- 2005. Society of Petroleum Engineers
- 5.8.6 Naturally Fractured Reservoir, 5.6.4 Drillstem/Well Testing, 4.6 Natural Gas
- 0 in the last 30 days
- 661 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Most of the theoretical work on decline-curve analysis with nonlaminar flowin the reservoir considers either a dry gas or liquid flow in a homogeneoussystem. The purpose of this work is to analyze decline curves considering thenon-Darcy flow effect in the reservoir for a slightly-compressible-liquid flowin dual-porosity systems at constant wellbore pressure.
The transient and boundary-dominated flow periods are examined by means ofcomputer results generated with a finite-difference simulator. Analyticalexpressions of velocity and wellbore rate are presented for the first time inthis paper. These equations contain the laminar-flow solution as a particularcase. A method is proposed to identify the presence of inertial effects byplotting d[log(q)]/d[log(t)] against log(t).
The method for area calculation under laminar conditions produces a goodapproximation for a reservoir under nonlaminar flow. However, the presence ofinertial effects distorts the shape of decline curves, resulting in erroneousestimates of wellbore and reservoir parameters by type-curve analysis withlaminar decline curves.
The utility of the methodology presented in this work is illustrated withsynthetic examples.
Most of the existing techniques available in the literature for determiningproductivities and reservoir parameters are based on two main assumptions:applicability of Darcy's law and constant inner-boundary condition, eitherconstant production rate or constant bottomhole flowing pressure. Neither ofthese assumptions is frequently fulfilled.
In a naturally fractured formation, we may have wells initially producing ata high rate and, in some cases, production declines after a few hours.Analyzing the transient flow-rate behavior will add more information to producea more complete evaluation. From an engineering viewpoint, the initial declinecould be a key factor in deciding whether to complete or abandon a well. Inhomogeneous systems, this decline is the only one observed, but for fracturedreservoirs, the initial decline does not always represent the final state ofdepletion.
At present, most of the reports on constant-bottomhole-pressure tests foundin the literature assume that only one phase flows in porous media and thatDarcy's law is applicable to both homogeneous and fractured reservoirs.
In cases in which Darcy's law is not valid, there are some works thatconsider different kinds of tests as well as different reservoir types. Refs.10 and 11 showed that inertial effects could be important in systems withslightly-compressible-liquid flow, providing analytical solutions for bothtransient and boundary-dominated flow. Nevertheless, there are no analyticalexpressions to analyze flow-rate responses for constant-bottomhole-pressuretests in naturally fractured reservoirs with non-Darcy flow. These expressionsare relevant if we take into consideration that inertial effects are expectedto occur mainly in the fracture system. The objective of this paper is topresent new analytical expressions for non-Darcy liquid flow in dual-porositysystems produced at constant bottomhole pressure.
|File Size||526 KB||Number of Pages||13|
1. Vásquez C., M.A.: "Análisis Transitorio de Pruebas a Gasto Variable enYacimientos Saturados." MS thesis, Div. de Estudios de Posgrado de la Facultadde Ingeniería de la UNAM, Mexico City (1995).
2. Da Prat, G.: Well Test Analysis for Fractured ReservoirEvaluation, Elsevier Science Publishing Co., New York City (1990).
3. Fetkovich, M.J.: "DeclineCurve Analysis Using Type Curves, " JPT (June 1980) 1065.
4. Da Prat, G., Cinco-Ley, H., and Ramey, H.J. Jr.: "Decline Curve Analysis Using TypeCurves for Two-Porosity Systems," SPEJ (June 1981) 354.
5. Sageev, A., Da Prat, G., and Ramey, H.J. Jr.: "Decline Curve Analysis forDouble-Porosity Systems," paper SPE 13630 presented at the 1985 SPECalifornia Regional Meeting, Bakersfield, California, 27-29 March.
6. Da Prat, G.: "Well Test Analysis for a Naturally Fractured Reservoir,"PhD thesis, Stanford U., Stanford, California (1980).
7. Ehlig-Economides, C.A. and Ramey, H.J. Jr.: "Transient Rate Decline Analysis forWells Produced at Constant Pressure," SPEJ (February 1981) 98.
8. Villalobos L.H.: "Análisis de Pruebas de Presión en YacimientosNaturalmente Fracturados Considerando el Efecto de Flujo de Alta Velocidad," MSthesis, Div. de Estudios de Posgrado de la Facultad de Ingeniería de la UNAM,Mexico City (1990).
9. Forchheimer, P.H.: "Wasserbewegung Durch Boden," Zeitz ver Deutsh Ing.(1901) 45, 1782.
10. Camacho-V., R.G., Vásquez-C., M.A., and Padilla-S., R.: "New Results on Decline CurvesConsidering Non-Darcy Flow Effects," SPEREE (October 1998) 457.
11.Camacho-V., R.G. et al.: "New Results on Transient Well TestAnalysis Considering Nonlaminar Flow in the Reservoir," SPEFE (December1996) 237.
12. Roldán C., J.L.: "Análisis de Datos de Presión con Efectos no Laminaresen Yacimientos Homogéneos," MS thesis, Div. de Estudios de Posgrado de laFacultad de Ingeniería de la UNAM, Mexico City (1996).
13. Rodríguez-R., J.: "Análisis de Curvas de Declinación de Producción enYacimientos Naturalmente Fracturados Considerando Flujo no Laminar," BS thesis,Facultad de Ingeniería de la UNAM, Mexico City (1996).
14. Geertsma, J.: "Estimatingthe Coefficient of Inertial Resistance in Fluid Flow Through Porous Media,"SPEJ (October 1974) 445.
15. Gewers, C.W.W. and Nichol, L.R.: "Gas Turbulence Factor in aMicrovugular Carbonate," J. Cdn. Pet. Tech. (April-June 1969) 51, 6.
16. Zwillinger, D.: Handbook of Differential Equations, AcademicPress Inc., Boston (1992).
17. Nayfeh, A.H.: Perturbation Methods, John Wiley & Sons Inc.,New York City (1973).
18. Zill, D.G.: Ecuaciones Diferenciales con Aplicaciones, GrupoEditorial Iberoamérica, Mexico City(1986).
19. Spiegel, M.E.: Transformadas de Laplace, McGraw-Hill de México,Mexico City (1982).
20. Boyce, W.E. and DiPrima, R.C.: Ecuaciones Diferenciales y Problemascon Valores en la Frontera, Editorial Limusa, Mexico City (1976).
21. Warren, J.E. and Root, P.J.: "The Behavior of Naturally FracturedReservoirs," SPEJ (September 1963) 245; Trans., AIME, 228.
22. Rodríguez-R., J., and Camacho-V., R.: "Avances en Curvas de Declinaciónen Yacimientos Naturalmente Fracturados," paper presented at the 2001 AIPMTechnical Conference, Comalcalco, Tabasco, Mexico, 9 September.
23. Horne, R.N.: Modern Well Test Analysis: A Computer-AidedApproach, Petroway, Palo Alto, California (1995).
24. Abramowitz, M. and Stegun, I.A.: Handbook of MathematicalFunctions , Dover, New York City (1964).